; ======================================================================
;
;          Structure and Interpretation of Computer Programs
;                  (trial answer to excercises)
;
;                  计算机程序的构造和解释(习题试解)
;
;                                             created: code17 03/05/05
;                                             modified:
; (保持内容完整不变前提下，可以任意转载)
; ======================================================================

;; SICP No.1.33

;; 递归版本
(define (filtered-accumulate-r filter combiner null-value term a next b)
  (if (> a b)
      null-value
      (combiner (if (filter a) (term a) null-value)
                (filtered-accumulate-r filter combiner null-value
                                       term (next a) next b))))

;; 迭代版本
(define (filtered-accumulate-i filter combiner null-value term a next b)
  (if (> a b)
      null-value
      (filtered-accumulate-i filter combiner
                             (if (filter a)
                                 (combiner null-value (term a))
                                 null-value)
                             term (next a) next b)))

;; 素数的平方和
(define (sum-of-primes-square a b)
  (define (next i) (+ i 1))
  (filtered-accumulate-r prime? + 0 square a next b))

;; 互质数的积
(define (product-of-relative-primes n)
  (define (relative-prime? i) (= (gcd i n) 1))
  (define (id i) i)
  (define (next i) (+ i 1)) 
  (filtered-accumulate-i relative-prime? * 1 id 2 next (- n 1)))


;; Test-it
;; Welcome to MzScheme version 209, Copyright (c) 2004 PLT Scheme, Inc.
;; > (sum-of-primes-square 3 10)
;; 83
;; > (product-of-relative-primes 10)
;; 189